To determine the ascending order of the fractions \( \frac{1}{3} \), \( \frac{4}{7} \), and \( \frac{2}{5} \), we can compare them by finding a common denominator or converting them to decimal form.

1. Convert each fraction to decimal:

- \( \frac{1}{3} = 0.333\ldots \) (repeating)
- \( \frac{4}{7} \approx 0.5714 \)
- \( \frac{2}{5} = 0.4 \)

2. Compare the decimal values:

- \( 0.333\ldots \) (for \( \frac{1}{3} \))
- \( 0.4 \) (for \( \frac{2}{5} \))
- \( 0.5714 \) (for \( \frac{4}{7} \))

In ascending order:

- \( \frac{1}{3} \approx 0.333\ldots \)
- \( \frac{2}{5} = 0.4 \)
- \( \frac{4}{7} \approx 0.5714 \)


The fractions in ascending order are:

\( \frac{1}{3} < \frac{2}{5} < \frac{4}{7} \)

So the correct answer is C. \( \frac{1}{3} < \frac{2}{5} < \frac{4}{7} \).